=207. Analysis of the active deposit.= The radio-active processes occurring in thorium are far more complicated than those in uranium. It has already been shown in chapter vi that a radio-active product Th X is continuously produced from the thorium. This Th X breaks up, giving rise to the radio-active emanation. The emanation produces from itself a type of active matter which is deposited on the surface of bodies, where it gives rise to the phenomena of excited or induced activity. This active deposit possesses some distinctive chemical and physical properties which distinguish it from the emanation and the Th X. We have seen (section 180) that the rate at which the active deposit loses its activity depends upon the time of exposure of the body made active to the emanation. The explanation of the activity curves for different time of exposure will now be considered. The curve of variation of activity for a short exposure of 10 minutes has already been given in Fig. 65. The activity is small at first but increases rapidly with the time; it passes through a maximum about 4 hours later, and finally decays exponentially with the time, falling to half value in 11 hours. This remarkable effect can be explained completely[301] if it be supposed that the active deposit consists of two distinct substances. The matter initially deposited from the emanation, which will be called thorium _A_, is supposed to be changed into thorium _B_. Thorium _A_ is transformed according to the ordinary exponential law, but the change is not accompanied by any ionizing rays. In other words, the change from _A_ to _B_ is a “rayless” change. On the other hand, _B_ breaks up into _C_ with the accompaniment of all three kinds of rays. On this view the activity of the active deposit at any time represents the amount of the substance _B_ present, since _C_ is inactive or active to a very minute extent. If the variation of the activity imparted to a body exposed for a short interval in the presence of the thorium emanation, is due to the fact that there are two successive changes in the deposited matter _A_, the first of which is a “rayless” change, the activity _I_{t}_ at any time _t_ after removal should be proportional to the number _Q_{t}_ of particles of the matter _B_ present at that time. Now, from equation (4) section 197, it has been shown that $$ Q = \frac {nλ_1} {λ_1 − λ_2} (e^{–λ_2 t} - e^{–λ_1 t}) $$ .... (4). The value of _Q_{t}_ passes through a maximum _Q_{T}_ at the time _T_ when $$ \frac {λ_2} {λ_1} − e^{-(λ_1–λ_2) T} $$ . The maximum activity _I_{T}_ is proportional to _Q_{T}_ and $$ \frac {I_t} {I_T} = \frac {Q_t} {Q_T} = \frac {e^{–λ_2 t} - e^{–λ_1 t}} {e^{–λ_2 T} − e^{–λ_1 T}} $$ .